# A horizontal rope pulls a 10kg wood sled across frictionless snow. A 5kg wood box rides on top of the sled. What is the largest tension force for which the box doesn't slip. Assume friction...

A horizontal rope pulls a 10kg wood sled across frictionless snow. A 5kg wood box rides on top of the sled. What is the largest tension force for which the box doesn't slip. Assume friction coefficient as 0.44

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jeew-m | College Teacher | (Level 1) Educator Emeritus

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When the wood sled start to travel due to the pull the small wooden box also start to travel. If we assume that tension force of rope is T then by the Newtons second law of motion ;

T = (5+10)*a where a is the acceleration.

When T increases acceleration will also increase. But initially the wooden box travel with the wood sled due to friction force between wood sled and wood box. When T increases maximum friction force the wooden box will start to slip.

Using F = ma to the whole system

`T_(max) = (5+10)*a`

`a = T_(max)/15 `

Since the small box travel together with the wood sled before it slips it has the same acceleration as the whole system.

Using F = ma to the small box at slip

friction force = m*a

`0.44*5*9.81 = 5*T_(max)/15 `

`T_(max) = 64.746N`

So the maximum tension of the rope is 64.746N

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